Rearranging Dyson-Schwinger equations / Karen Yeats.

Format:

Book

Author/Creator:

Yeats, Karen, 1980- author.

Series:

Memoirs of the American Mathematical Society ; Volume 211, Number 995.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 211, Number 995

Language:

English

Subjects (All):

Feynman diagrams.

Quantum field theory--Mathematics.

Quantum field theory.

Physical Description:

1 online resource (82 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2010.

Language Note:

English

Summary:

Dyson-Schwinger equations are integral equations in quantum field theory that describe the Green functions of a theory and mirror the recursive decomposition of Feynman diagrams into subdiagrams. Taken as recursive equations, the Dyson-Schwinger equations describe perturbative quantum field theory. However, they also contain non-perturbative information. Using the Hopf algebra of Feynman graphs the author follows a sequence of reductions to convert the Dyson-Schwinger equations to a new system of differential equations.

Contents:

""Contents""; ""Abstract""; ""Foreword""; ""Preface""; ""Chapter 1. Introduction""; ""Chapter 2. Background""; ""2.1. Series""; ""2.2. Feynman graphs as combinatorial objects""; ""2.3. Feynman graphs as physical objects""; ""Chapter 3. Dyson-Schwinger equations""; ""3.1. B+""; ""3.2. Dyson-Schwinger equations""; ""3.3. Setup""; ""Chapter 4. The first recursion""; ""4.1. From the renormalization group equation""; ""4.2. From SY""; ""4.3. Properties""; ""Chapter 5. Reduction to one insertion place""; ""5.1. Colored insertion trees""; ""5.2. Dyson-Schwinger equations with one insertion place""

""Chapter 6. Reduction to geometric series""""6.1. Single equations""; ""6.2. Systems""; ""Chapter 7. The second recursion""; ""7.1. Single equations""; ""7.2. Systems""; ""7.3. Variants""; ""Chapter 8. The radius of convergence""; ""8.1. Single equations""; ""8.2. Systems""; ""8.3. Possibly negative systems""; ""Chapter 9. The second recursion as a differential equation""; ""9.1. P(x)=x""; ""9.2. QED as a single equation""; ""9.3. Results on global solutions""; ""9.4. The running coupling""; ""Bibliography""; ""Index""

Notes:

"Volume 211, Number 995 (end of volume)."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-0612-8